Devin throws a football 7 1/3 yards. Carl throws it 2 1/2 times farther. How much farther did Carl's throw travel than Devin's?

The graph of g(x) is on the image at the end, and the correct option for the transformation is B.

We define a horizontal dilation of scale factor k as:

g(x) = f(k*x)

if k > 1, we have a stretch.

if  0 < k < 1, we have a shink of scale factor 1/k

Here we have:

g(x) = f (5x) = 5x - 4

We can notice that k = 5, then we have a stretch, thus, the correct option is B.

The graph of function g(x) can be seen in the image at the end.,

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Answer:

B

Step-by-step explanation:

Subtracting second equation from first, term by term , gives

(8x - 4x) + (3y - 3y) = (14 - 8) , that is

4x + 0 = 6, so

4x = 6 → B

Answer:

student ticket = $11

(adult ticket = $15)

Step-by-step explanation:

Let a = price of adult ticket

Let s = price of student ticket

Given:

⇒ 12a + 11s = 301

Given:

⇒ 6a + 4s = 134

Multiply 6a + 4s + 134 by 2 then subtract from 12a + 11s = 301 to eliminate a:

⇒ (6a + 4s = 134) × 2:  12a + 8s = 268

  12a + 11s = 301

- (12a + 8s = 268)

--------------------------

            3s = 33

⇒ s = 33 ÷ 3 = 11

Substitute found value of s into one of the equations and solve for a:

⇒ 12a + 11(11) = 301

⇒ 12a + 121 = 301

⇒ 12a = 180

⇒ a = 15

Therefore, the price of an adult ticket is $15 and the price of a student ticket is $11

Answer:

n = -3

Step-by-step explanation:

-5n-30=21+9n+3n

-5n-30=21+12n

-17n=51

n=-3

Answer:

- 14j -10. the answer online

The population will be in 2046 is, 246,935.

What is increase in population?

Human population growth is the rise in the total number of people on the planet. Our population numbers was largely steady for the majority of human history. The availability and dependability of energy, food, water, and medical care increased with invention and industrialization.

Given: Springfield's population in 2019 was 202628 people and is projected to grow at a rate of 0.81% each year.

The population growth is increase constantly.

We have to find the population in 2046.

As population increase by 0.81% each year.

That means for each year population increase by

202628 x 0.81% = 202628 x 0.0081 = 1641.29 ≈ 1641

⇒ For each year population increase by 1641 people.

Between 2019 to 2046 there are 27 years.

After 27 years population increase by 27 x 1641 = 44307  people.

So, the total population in 2046 is, 202,628 + 44,307 = 246,935.

Hence, the population will be in 2046 is, 246,935.

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Answer:

64cm³

Step-by-step explanation:

( 4 x 4 x 4) cm x cm x cm

Answer: $57.6

Step-by-step explanation:

Given : A businesswoman sells a bag for $52.32.

Let cuurent selling price : SP = $52.32

As they are making 9% profit now.

That means SP= Cp +0.09 CP , where Cp is the cost price of bag.

i..e \(52.32=Cp(1+0.09) \ \text{[Substituted value of SP in LHS and taking Cp common outside in RHS]}\)

\(\Rightarrow\ 52.32=Cp(1.09)\Rightarrow\ CP=\dfrac{52.32}{1.09}=48\)

i..e Cost price of bag = 48

Selling price to gain 20% profit = Cp+0.20CP

= CP(1+0.20)

=48 (1.20)

= 57.6

Hence, the  selling price the businesswoman should ask in order to make 20% profit​ = $57.6

Step-by-step explanation:

all points on the x axis have a y value of 0.

so, we need to find all points (x, 0) with a distance of 16 to (4, -8).

the distance to a point is the Hypotenuse of the right-angled triangle with the coordinate differences as legs.

and so Pythagoras applies :

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle).

so, in our case we have

16² = (4-x)² + (-8 - 0)²

256 = 16 - 8x + x² + 64 = x² - 8x + 80

x² - 8x - 176 = 0

if we have no other idea of factorization the general solution of such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -8

c = -176

x = (8 ± sqrt((-8)² - 4×1×-176))/(2×1) =

= (8 ± sqrt(64 + 704))/2 = (8 ± sqrt(768))/2 =

= (8 ± sqrt(256×3))/2 = (8 ± 16×sqrt(3))/2 =

= 4 ± 8×sqrt(3)

x1 = 4 + 8×sqrt(3) = 17.85640646...

x2 = 4 - 8×sqrt(3) = -9.856406461...

so, the points on the x axis that are 16 units apart from (4, -8) are

(x1, 0) and (x2, 0)

I am not sure in what format you need the answer.

please fill in for x1 and x2 from above what you need.

The round trip distance in miles from city 1 to city 3 is given as follows:

30 miles.

The matrix corresponding to the distances between each of the cities is given by the image presented at the end of the answer.

Looking at row 1, column 3, we have that the distance from city 1 to city 3 is of 15 miles.

For the round trip distance, we have to go back from city 3 to city 1, more 15 miles, hence the distance is given as follows:

2 x 15 = 30 miles.

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The conic section of the equation 4x² + 9x +4y² - 36y - 125 = 0 is a circle

The given equation is

4x² + 9xy + 4y² - 36y - 125 =0

The above equation is an illustration of a circle equation

The standard form of a circle equation is

(x - a)² + (y - b)² = r²

Where

(a, b) is the center

r is the radius

While the general form of the equation is

ax² + fx + by² + gy + c =0

Where c is a constant

Recall that, we have

4x² + 9x + 4y² - 36y - 125 =0

This is the general form

We can convert to the standard form as follows

Divide through by 4

x² + 2.25x + y² - 9y - 31.25 =0

Next, we complete the square of the x-terms and the y-terms

For the x-terms, we have

x² + 2.25x = x² + 2.25x + (2.25/2)² - (2.25/2)²

x² + 2.25x = (x + 2.25/2)² - (2.25/2)²

For the y-terms, we have

y² - 9y = y² - 9y + (9/2)² - (9/2)²

y² - 9y = (y - 9/2)² - (9/2)²

Substitute the new x and y terms

So, x² + 2.25x + y² - 9y - 31.25 = 0 becomes

(x + 2.25/2)² - (2.25/2)² + (y - 9/2)² - (9/2)²- 31.25 =0

Evaluate the sum of like terms

(x + 2.25/2)² + (y - 9/2)² - 3377/64 = 0

So, we have

(x + 9/8)² + (y - 9/2)² = 3377/64

Using the above as a guide, we can conclude that the conic section of the equation is a circle

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Answer:

H0: Ud >= 0

H1: UD < 0

Step-by-step explanation:

We have the sample size = 81

Mean of x = 107

The alpha level was not given for me to help you calculate further.

This researcher wants to know if increasing reading speed brings about a decrease in the comprehension of the reader.

The hypothesis are

Null hypothesis

H0: U >= 0

Alternative hypothesis

H1: U < 0

Thank you

Answer:

3

Step-by-step explanation:

√83-√35 = 3.1943537960446828393782978131270521416836379374706155296172187959...

Step-by-step explanation:

we need to remember the squared numbers of the baud integers :

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

so, what squared integers are closest to 83 and 35 ?

well, 81 (9²) and 36 (6²).

so, the result has to be closest to 9 - 6 = 3.

83 is larger than 81 than 35 is smaller than 36. so, 3 is less than sqrt(83) - sqrt(35).

therefore, the correct answer is indeed 3.

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

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Answer:

PQ and RS are parallel to each other

Step-by-step explanation:

Slope of two points (x1,y1) and (x2,y2) is given by

slope = (y2-y1)/(x2-x1)

Lets find the slope of PQ and RS

for PQ P(2, -1), Q(-3,-1), R(-11, 9), S(-7, 9)

slope PQ = (-1 -(-1))/(-3 -2) = (-1 + 1)/5 = 0/5 = 0

Slope RS = (9-9)/(-7 - (-11) ) = 0/4 = 0

Since

slope PQ = slope RS = 0

Hence PQ and RS are parallel to each other

If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Mr. Olsen has a PC business wherein he sells everything at 44.5% above the wholesale price. On the off chance that he bought a printer for $80 wholesale.

Then the retail price is given as,

⇒ $80 x (1 + 0.445)

⇒ $80 x 1.445

⇒ $115.60

If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.

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Yes, cropping a picture and then using a scale factor to resize it is a two-step process.

The image is first cropped by subtracting 2 inches from the right side, altering the image's proportions.

The image is then enlarged using a scale factor of 1.5, which increases the image's dimensions by 1.5.

The final measurements of the image would be its original measurements less 2 inches (for cropping), then multiplied by 1.5. (for the resizing).

It's vital to keep in mind that both picture cropping and image scaling change the size of the final product.

Yes, cropping a photo, then resizing it with a scale factor, is a two-step process.

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The value of variable 'v' in the expression ( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2 is equal to -4.

The expression is equal to,

( v - 2 ) / (2v² + 10v ) + 1 / ( 2v + 10 ) = 1 / 2

Simplify the expression we have,

⇒ ( v - 2 ) / 2v ( v + 5 ) + 1 / 2( v+ 5 ) = 1 / 2

Take the least common multiple of the denominator we have,

⇒ [( v - 2 ) + 2 ] / 2v( v+ 5 ) = 1 / 2

⇒ v  / 2v( v+ 5 ) = 1 / 2

Multiply both the sides of the expression by 2 we get,

⇒ 1 / 2( v+ 5 ) = 1 / 2

⇒ 1 /( v + 5 ) = 1

Cross multiply the expression we get,

⇒ v + 5 = 1

Subtract 5 from the both the sides of the equation we get,

⇒ v = -4

Therefore , the value of v in the given expression is equal to -4.

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To calculate the prorations for interest and property taxes, we need to determine the number of days each party (the buyer and the seller) will own the property during the month of June.

There are a total of 30 days in June, so the seller will own the property for 15 days (from June 1 to June 15), and the buyer will own the property for 15 days (from June 16 to June 30).

Prorations for Interest:

The annual interest rate is 8%, which means the monthly interest rate is 8%/12 = 0.6667%. To calculate the daily interest rate, we divide the monthly interest rate by 30 (the number of days in June):

0.6667% / 30 = 0.0222%

The total interest owed for the full month is:

$168,745.60 x 0.6667% = $1,124.28

To calculate the prorated interest for the seller, we multiply the daily interest rate by the number of days the seller owned the property:

0.0222% x $168,745.60 x 15 = $559.02

To calculate the prorated interest for the buyer, we multiply the daily interest rate by the number of days the buyer will own the property:

0.0222% x $168,745.60 x 15 = $559.02

Therefore, the total prorations for interest are:

$559.02 for the seller and $559.02 for the buyer.

Prorations for Property Taxes:

To calculate the prorated property taxes, we divide the annual taxes by 365 (the number of days in a year) to get the daily tax rate:

$3,893.25 / 365 = $10.66 per day

To calculate the prorated property taxes for the seller, we multiply the daily tax rate by the number of days the seller owned the property:

$10.66 x 15 = $159.90

To calculate the prorated property taxes for the buyer, we multiply the daily tax rate by the number of days the buyer will own the property:

$10.66 x 15 = $159.90

Therefore, the total prorations for property taxes are:

$159.90 for the seller and $159.90 for the buyer.

The prorations will be subtracted from the seller's equity because they represent expenses incurred by the seller during the time they owned the property.

There are 6 DIFFERENT POSSIBLE arrangements as obtained using the factorial method and they are :

DMC, CMD, DCM, MDC, CDM, MCD

Given :

DETECTIVE STORY = D

MYSTERY STORY = M

COMIC BOOK = C

To use the factorial method, we find the factorial value of the number of books to be arranged

Number of different possible arrangements = (number of books)!

Number of books = 3

Hence, 3! = 3 * 2 * 1 = 6 ways

The sample space :

DMC

CMD

DCM

MDC

CDM

MCD

THEREFORE, there are 6 different samples on the SAMPLE SPACE.

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Answer:

63 m/s

Step-by-step explanation:

h(3) = 3(3)² + 36(3) + 300 = 435

h(6) = 3(6)² + 36(6) + 300 = 624

v = Δh/Δt = (624m - 435m) / (6s - 3s) = 63 m/s

Answer:

It is best to solve a system of equations using substitution when one of the equations isolates one of the variables, or when the coefficient of one of the variables is 1 or -1.

Step-by-step explanation:

This makes it easier to substitute one variable for the other, allowing you to solve for the remaining variable. It is also a good idea to check the solution back in the original equations just to make sure it is a valid solution

Answer:

Answer Below

Step-by-step explanation:

It is best to use substitution if one of the variables is isolated or has a coefficient of 1 or -1.

Answer: $1.50

Step-by-step explanation: 1. subtract the 3.25 from 4.50 to get a difference that is the price of the added hotdog 2. now that you know each hot dog cost $1.25 you can do 3.25 - 2(1.25) to get 0.75 which is the price of one soda. 3. You can no multiply $0.75 by two (the amount of sodas) to get the answer $1.50.

A.

1. Mode: No mode. Median: 24. Mean: 30.875. Range: 50.

2. Mode: No mode. Median: 33.5. Mean: 43.9. Range: 85.

3. Mode: No mode. Median: 46. Mean: 43.571. Range: 61.

4. Mode: No mode. Median: 17. Mean: 18. Range: 28.

5. Mode: No mode. Median: 10.5. Mean: 13.5. Range: 27.

6. Mode: 15. Median: 22.5. Mean: 25.857. Range: 31.

B.

7. Mode: 4.3. Median: 4.2. Range: 2.1.

8. Mode: 18.6. Median: 18.6. Range: 0.8.

C.

9. Mode: No mode. Median: 4/9.

10. Mode: No mode. Median: 5/24.

The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Sample space is a set of all possible outcomes of an experiment or random event. It is the collection of all possible results or outcomes that can occur when a particular event is performed.

In the given question,

The sample space is the set of all possible outcomes of an experiment. In this case, the experiment is rolling a fair 12-sided die. The sample space would include all possible values that the die can land on when rolled.

Since a 12-sided die has 12 equally likely outcomes, the sample space would consist of the numbers 1 through 12. However, only one of the options presented in the question includes all 12 numbers in the sample space, which is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Option S = {1, 2, 3, 4, 5, 6} represents the sample space of a regular 6-sided die, while options S = {1} and S = {12} only include one possible outcome, which is not applicable for a 12-sided die.

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Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

A variable is anything that may be altered in the context of a mathematical notion or experiment. Variables are frequently denoted by a single symbol. .

a. Input variables: hours worked as a cashier, payroll clerk, and assistant.

The total amount earned each week is the output variable.

b. To determine the weekly total, multiply the number of hours worked at each job by the hourly rate and put them together. As a result, the equation would be:

Total weekly wage = (hours worked as a cashier x cashier hourly rate) + (hours worked as a payroll clerk x payroll clerk hourly rate) + (hours worked as an aide x rate per hour as an aide)

c. The amount of hours worked as an assistant is always 10 hours fewer than that of a payroll clerk. Therefore, if x denotes the number of hours worked as a payroll clerk, then the number of hours worked as an assistant may be denoted as (x - 10).

d. The equation describing the total money earned each week is as follows:

(20 x 9.5) + (x x 9) + ((x - 10) x 7) = y

This expression is simplified as follows:

y = 190 + 9x - 70 + 7x

y = 16x + 120

Hence the output variable (total weekly earnings) is a function of the input variable (number of hours worked as a payroll clerk) and may be expressed by the equation y = 16x + 120.

f. The realistic replacement values for x would be determined by the maximum number of hours you may work at each job as well as the amount of time available to work. Working 8 hours as a payroll clerk may be a reasonable substitute value if you have restricted availability, but 50 hours is unlikely.

g. If you do not work as an aide, you may calculate your total weekly income by setting the number of hours worked as an aide to zero in the calculation for the total amount earned each week. This results in:

y = 16x + 120 + 0

y = 16x + 120

As a result, the total weekly wage would be determined only by the number of hours performed as a cashier and payroll clerk.

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The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

The table below shows the ratios of boxed donuts to the cost.

Donuts    A       4        5     C

Cost    13.80  27.60   B   55.20

Now, By definition of ratio, we get;

⇒ A / 13.80 = 4 / 27.60

⇒ A = 13.80 × 4 / 27.60

⇒ A = 2.00

And,

⇒ 4 / 27.60 = 5 / B

⇒ B = 5 × 27.60 / 4

⇒ B = 34.5

⇒ 4 / 27.60 = C / 55.20

⇒ C = 55.20 × 4 / 27.60

⇒ C = 8

Thus, The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

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Answer:

a

Step-by-step explanation:

i took the test :)